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# 数学代写|金融数学代写Financial Mathematics代考|MATH3090 What Is Market Impact?

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## 数学代写|金融数学代写Financial Mathematics代考|What Is Market Impact?

There are several definitions of market impact, some are more insightful than others. One that is general and more intuitive is:
Market Impact is the cumulative market-wide response of the arrival of new order flow.
This definition incorporates the effect of both trades and order submissions (or cancellations). It also includes the effects that, while changing the overall system “hidden state,” do not immediately lead to a price change. There are several likely components to this response:

• The first is a purely “mechanical” one. The removal of liquidity, either via a trade or via a cancellation, can lead to change in the prevailing mid-price.
• The second is “economic related.” Any change in the shape of the order book alters the supply/demand sides leading to a re-establishment of local equilibrium price.
• Another component can be called “speculative.” A price move may lead participants to expect the initiation (or continuation) of a momentum trend, triggering some “copycat” trading in the same direction.
• Then there is an “arbitrage” component where participants try to step in to provide liquidity in prevision of the price move and immediately get out of it at a better price.
These effects are then propagated through the system with various levels of feedback loops leading to very complicated “chaos-like” macro market dynamics. There is also evidence that these effects are amplified by the “novelty” of the price move meaning that the behavior can be highly path dependent.

## 数学代写|金融数学代写Financial Mathematics代考|Modeling Transaction Costs (TC)

As discussed, MI is a quantity that cannot be directly observed but can be inferred. What is observed are the prices that one pays to execute an order of a certain size, for a particular instrument, over a specified time period. These prices incorporate different components that can be broadly grouped into specific categories:

1. Explicit Costs: These costs, in theory at least, are known in advance. These include exchange fees, clearing costs, taxes, etc. They also include all the fixed costs for connectivity, for accessing market data, etc. Part of these costs are independent of how the order is traded and depend only on the number of shares traded and total notional value (e.g., clearing fees, taxes). Other costs vary with implementation because they depend on the choice of venue (different venues have different fee schedules) and the order aggressiveness (in most venues one is charged to take liquidity, while receiving a rebate for providing liquidity).
2. Spread Costs: It is often necessary to cross the spread to take liquidity and the price achieved is thus higher than the prevailing price (usually defined as the midpoint). If the order is executed passively, the spread cost could be negative.
3. Exogenous Price Evolution: At the risk of oversimplifying, this is the theoretical price path that would have happened had we not traded.
4. Market Impact, as defined in the previous sections.

## 数学代写|金融数学代写Financial Mathematics代考|What Is Market Impact?

• 第一个是纯粹的“机械”。通过交易或取消取消流动性可能会导致现行中间价发生变化。
• 第二个是“经济相关”。订单簿形状的任何变化都会改变供需双方，从而导致重新建立​​局部均衡价格。
• 另一个组成部分可以称为“投机”。价格变动可能导致参与者预期动量趋势的启动（或持续），从而引发一些相同方向的“模仿”交易。
• 然后是“套利”部分，参与者试图介入以提供流动性以预测价格变动并立即以更好的价格退出。
然后，这些影响通过具有不同级别反馈循环的系统传播，导致非常复杂的“类似混沌”的宏观市场动态。还有证据表明，价格变动的“新颖性”会放大这些影响，这意味着行为可能具有高度的路径依赖性。

## 数学代写|金融数学代写Financial Mathematics代考|Modeling Transaction Costs (TC)

1. 显性成本：至少在理论上，这些成本是事先已知的。这些包括交易所费用、清算成本、税收等。它们还包括连接、访问市场数据等的所有固定成本。部分这些成本与订单的交易方式无关，仅取决于交易的股票数量和总名义价值（例如，清算费、税金）。其他成本因实施而异，因为它们取决于场地的选择（不同的场地有不同的费用表）和订单积极性（在大多数场地中，一个人被收取流动性费用，同时因提供流动性而获得回扣）。
2. 点差成本：通常需要交叉点差以获取流动性，因此获得的价格高于现行价格（通常定义为中点）。如果订单被动执行，点差成本可能为负。
3. 外生价格演变：冒着过于简单化的风险，这是如果我们不进行交易就会发生的理论价格路径。
4. 市场影响，如前几节所定义。

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